A constitutive law for snow taking into account the compressibility

Abstract

A constitutive law for snow derived from a complementary power potential is proposed. The total deformation of snow is divided into elastic and creep parts. A hereditary integral using Norton’s power law is employed to describe primary creep. The concept of effective stress, which takes compressibility of snow into account, is used to calculate creep deformation. The hereditary integral is approximated by a non-linear spring–dashpot model. Results from uniaxial compression experiments (stress range 15– 45 kPa) on sieved snow of density range 180–470 kgm-3 were used to determine the constants appearing in the constitutive equation. The response of snow to constant strain rate (7.4×10-6 s-1 to 2.2×10-5 s-1) under bilaterally confined conditions was found with an iterative scheme employing the proposed constitutive law. The simulated results agree well with the measured axial stresses and volumetric changes.

Study on the Constitutive Equation and Mechanical Properties of Natural Snow under Step Loading

“…Snow is composed of three phases of water, air, and ice connected together in the form of particles, and has a certain strength [13]. Subsequently, many experimental studies on snow have been conducted and various constitutive equations have been developed to understand snow deformation under loading conditions [14,15]. At present, the constitutive equations of snow can be divided into two kinds.…”

“…Mishra and Mahajan [14] considered that snow deformation consists of elastic deformation and creep deformation, ignoring time-hardening and microstructural changes. They described the constitutive relationship of snow based on a complementary power potential, which also predicted volume changes in snow samples.…”

“…In previous studies, the constitutive model of snow is frequently investigated using relative theoretical derivations or numerical simulation methods [14,26], and then verified by experimental data. However, the numerous parameters and complex formulas involved in these methods make them difficult to compute.…”

Stress measurements in the weak layer during snow stability tests

“…The damping of stress during the process of snow compaction can be attributed to the absorption of energy during plastic deformation of snow that is especially pronounced when untouched snow is loaded (Schweizer and others, 1995;Kronthaler and others, 2018). Indeed, when modeling the deformation of snow, Mishra and Mahajan (2004) divided deformation into an elastic and a creep part, the latter including the compressibility of snow.…”

Digital 3D Animation of Powder-Snow Avalanches

“…In such cases, the models borrow characteristics from other physical phenomena, such as granular and viscoplastic flows (TAI; HUTTER; GRAY, 2001;ANCEY, 2001;NICOT, 2004). Examples of rheological models used in snow applications are the Burgers model for viscoelastic materials (MELLOR, 1974), models for elastoplastic materials (SINGH et al, 2022;GAUME et al, 2019), models based on the micro-structural configuration of snow (St. Lawrence;LANG, 1981;BROWN, 1993), and models considering the compressibility of snow (MISHRA; MAHAJAN, 2004). Refer to Salm (1982) for more details on the earlier approaches of constitutive models for snow.…”